Suslin homology via cycles with modulus and applications

TL;DR

This paper establishes an equivalence between Chow groups of 0-cycles with modulus and Suslin homology for smooth projective varieties with divisors, providing new insights and answering open questions in algebraic geometry.

Contribution

It proves the isomorphism between Chow groups with modulus and Suslin homology under certain conditions, linking two important invariants in algebraic geometry.

Findings

Chow group of 0-cycles with modulus equals Suslin homology under specified conditions

Derived several consequences and applications of this equivalence

Provided an answer to a question posed by Barbieri-Viale and Kahn

Abstract

We show that for a smooth projective variety $X$ over a field $k$ and a reduced effective Cartier divisor $D \subset X$, the Chow group of 0-cycles with modulus $\mathrm{CH}_0(X|D)$ coincides with the Suslin homology $H^S_0(X \setminus D)$ under some necessary conditions on $k$ and $D$. We derive several consequences, and we answer to a question of Barbieri-Viale and Kahn.